In part A of the experiment a hair is illuminated with a laser and a diffraction pattern is observed. The wavelength λ = 624 nm and the pattern is projected on to the wall a distance L = 2.3 m from the hair. The distance across the central maximum is measured to be 2y= 0.051 m.Calculate the width of the hair in µm (1x10-6m) to one decimal place. You do not need to specify the units.
Question
In part A of the experiment a hair is illuminated with a laser and a diffraction pattern is observed. The wavelength λ = 624 nm and the pattern is projected on to the wall a distance L = 2.3 m from the hair. The distance across the central maximum is measured to be 2y= 0.051 m.Calculate the width of the hair in µm (1x10-6m) to one decimal place. You do not need to specify the units.
Solution
To calculate the width of the hair, we can use the formula for single-slit diffraction:
d = λL / 2y
where: d is the width of the hair, λ is the wavelength of the light, L is the distance from the hair to the wall, and 2y is the distance across the central maximum.
Substituting the given values:
d = (624 x 10^-9 m) * (2.3 m) / (0.051 m)
Solving this equation gives:
d = 2.81 x 10^-5 m
Converting this to micrometers (1 µm = 1 x 10^-6 m) gives:
d = 28.1 µm
So, the width of the hair is approximately 28.1 µm to one decimal place.
Similar Questions
In part A of the experiment a pair of slits are illuminated with a laser and an interference pattern is observed. The slit spacing is d = 0.0001 m and the pattern is projected on to the wall a distance L= 2.23 m from the slits. From one dark spot 7 further dark spots are counted and the distance is measured to be Z = 0.097 m.Calculate the wavelength λ of the laser.Express answer in nm (1x10-9m) to the nearest whole number.
What is the size comparison of one nanometer to the width of a human hair?a.1:10,000b.1:10c.1:100,000d.1:1,000
In part A of the experiment a pair of slits are illuminated with a laser and an interference pattern is observed. The slit spacing is d = (0.100 ± 0.003) mm and the pattern is projected on to the wall a distance L= (2.352 ± 0.02) m from the slits. From a dark spot 8 further dark spots are counted and the distance is measured to be Z = (12.2 ± 0.4) cm.The wavelength of the laser is calculated to be λ = 648 nm.Calculate the uncertainty in the wavelength. Express answer in nm (1x10-9m) to the nearest whole number.
In part B of the experiment a Michelson Interferometer is used to determine the wavelength λ of the laser. An interference pattern is observed due to the light being split into two paths with slightly different lengths.A vacuum chamber (of length d) is placed in one of the paths and the air pumped out. Then as air leaks back into the chamber the number of fringes, N, that pass a certain point are counted as the interference pattern changes.The following measurements were taken:N= 64 ± 5d= (0.077 ± 0.006) mThe wavelength λ of the laser is calculated to be 650 nm (using the value of the refractive index of air n given in the lab manual). Calculate the uncertainty of the wavelength λ of the laser in nm to the nearest whole number.
Q6: Suppose your hair grows at the rate 1/32 in per day. What is the rate at which it grows in nanometers per second? [1 in = 2.54 cm, 1 d = 86 400 s, and 109 nm = 1 m] (a) 92.0 nm/s (b) 91.9 nm/s (c) 9.2 nm/s (d) 91.0 nm/s (e) 919.0 nm/s Q7: The JCR of a student hostel is 50.0 ft long and 26 ft wide and has 8.0-ft high ceilings. What is the volume of the interior of the room in cubic centimeters? [1 ft = 0.304 8 m]. (a) 2.94 × 103 cm3 (b) 3.17 × 103 cm3 (c) 2.94 × 108 cm3 (d) 2.9 × 108 cm3 (e) 2.98 × 108 cm3 4
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.